More Spatio-Temporal Maps

Last night I came across a spatio-temporal map on the web showing travel time back 200 years ago or so. I can’t find the page, so we’ll have to let the when slide. I should have put the citation on the graphic itself. Note to processes.

As a kid, we’d be out of country for a long time. We’d maintain our connections to America via the Sears catalogue, the Armed Forces (radio) Network, and the movies that ran at the base theater. And, something called white bread. I was great stuff unlike white bread you buy at the grocery store today. We’d fly out of McGuire AFB in New Jersey. Once we flew out of somewhere else. But, we’d always fly back to McGuire. We’d end up in Newark, and Brooklyn Heights in NYC. More germane, we’d drive from New Jersey to the Alabama-Florida border where the stateside family lived.

The first time we came back it was on a boat. The next time we went it was on a prop plane. The next time it was on a jet. A week got compressed into a few hours…. But, here we were in New Jersey driving the interstates. They didn’t go everywhere. We never picked the places we were going so they were right off the interstates. No. We drove through lots of little towns. Lots of zigs and zags. Lots of late nights leaving the pitch black, entering the neon-lit burges, plunging back into the pitch black. There was a whole lot of spatio-temporal. Like that country song, “The world must be flat, people leave town and never come back….” Not really, but when they leave a product, they never come back.

So on to the map.

spatio-temporal map

Notice that we are talking land travel times, and earliest possible arrivals. Had they put travel by ship on here, the maps would be different. Travel and communications constraints made for dialect. You talked like all the people in your town. Widening that to say, your state wouldn’t make much sense, since different parts of your state where reached on different days. Your town might be isolated like far northwest South Carolina, which might be on the other side of the Appalachian mountains from the rest of the state. Those mountains were a considerable constraint. You went where the trails went, where the roads went, and before the railroads, you went where the canals and rivers went. Maybe you had a horse and went where the hell, you wanted to go.

Your travels where not a random walk. They were typically Levy flights. You were already in a fractal space. You were already in a world filled with Bayesian priors, unless of course, Joe of Joe’s Garage fame said, “Oh, no sir, you can’t get there from here.” Laugh, except that in the middle of the night, pre-interstate, east bound out of New Orleans, it was true. Dad always got lost there. But, don’t take my word for it. Try driving EB White’s coastal Maine.

Joe was just injecting some Gaussian noise, aka randomness into your Bayesian priors. So why do I not stop for directions?

But we are lucky, someone before us built roads, bridges, and tunnels. That “You can’t get there from here, not today.” was real. Today, we build stores and magazine stands on the side of an internet cable, on top of some API, running in one or more clouds somewhere on who knows how many servers at any given moment. We have a standard platform. We have whole product. When we improve it, those elevation lines on the map get closer together. When we improve it, we create wealth, create a monopoly, capture some cash, and become hero’s for some part of fifteen minutes. Being a hero twice doesn’t get you another fifteen minutes of fame. The terrain is out there. We just don’t have a mapping company willing to take on that project. No areal photos, no maps–apparently.

Notice the unknown, aka six weeks and beyond. There were keywords out there egging people on. The Santa Fe Trail, oh, yeah, a wide patch of grass in an otherwise rocky terrain. Follow the grass. Follow the wagon up ahead. Imagine having a teenager in your wagon. That fuzziness we reach at the six week mark is where that Gaussian normal and our Bayesian normal fight it out for statistical significance. Where our Poisson distributions and associated vectors leave us in the creative moment of creating a generative grammar for those following us. “Yeah, the lore says, cross this river to the south.” So another wagon shifts to the south. The rest of the wagons following that one shift as well. Tomorrow’s wagons, who knows.

Those elevation lines are still relevant today. I know that the drive through Chicago took three hellish hours, and that Erie, PA, I’d call it a day–a long spatio-temporal day of topological transforms. “It looked straight, until I changed maps.” Like, trying to drive west in Maryland or north in Nebraska. “You can’t get there from here.” Well, not until we put the interstate through. When we upgrade our roads, the steep, up and down two-lanes cut the hill tops off for fill, the bottoms get culverts and fill, the lanes multiply–the experience becomes flat. The same thing happened on the internet. Expectations rise. And, our look back machine considers the old stuff as lame, but back then it wasn’t lame–a historical elevation line runs through that.

The map above aggregated the data from tons of travelers. The data wasn’t just where New Yorkers went.

That added day running through north central Alabama was a mountain range between Huntsville and Birmingham. People in Huntsville don’t drive the hour or hour and a half to jobs in Birmingham. Yet, people make those kinds of drives in Houston all the time. Flat matters. In Houston, the roads a likely to be under water. Building culverts matter.

The map shows populations connecting to other populations. Your personal map is covered by a single normal with a lot of vectors an Poisson distributions under it. Look up into the sky. You don’t see the distributions you’re under., not a single one.  The technology adoption lifecycle connects a few highly related populations. The Bayesian terrain is there. The typical corporation have their economies of scale, reusable populations. Reusing populations means discontinuous innovations are out. It means you’re stuck in NYC even as every other non-local elevation line got erased.

Our product road maps tend to be straight lines. Having no topological map, we don’t built s-curves to gently get us over the next mountain. No, we drive straight ahead into the ditch. Well, at least you drove past the party at the rest area.

That one week travel time elevation line has moved all the way to the west coast with pockets still isolated as ever in between.

Innovation eliminates or reduces the impact of a constraint. What you see on the old map was time being lost to physical constraints, constraints on transportation and communications, constraints on getting there and getting done. Knowing what the situation today shows us how successful or innovations in roads, bridges, tunnels, and culverts have been. You don’t have to have taken the road trip or have gotten lost on Hwy-90 to know that those innovations have moved the constraints many times in your lifetime. It happens close to home, right in the street in front of your house, and the utility right-of-way behind your house. It happens in your house, in the walls, in the unused telephone connections, and wifi. It happens right behind your screen. All of it will continue to change. It’s not a matter of putting up another retail store, or serving the consuming masses. Mostly, it’s about getting a map. Find an elevation line and move it.

Lets hope we can get there from here.



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